1. For the given transformation, T: R³ → R², T(x, y, z) = (3x-2z, 2y - z) -> a) Find the standard matrix A for the linear transformation T. b) Use A to find the image of the vector v = (0,1,1). 2. Given the matrix A = [6] and P = [1 find A5 using a diagonal matrix D = P-1 AP.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. For the given transformation,
T: R³ → R², T(x, y, z) = (3x-2z, 2y - z)
->
a) Find the standard matrix A for the linear transformation T.
b) Use A to find the image of the vector v =
(0,1,1).
Transcribed Image Text:1. For the given transformation, T: R³ → R², T(x, y, z) = (3x-2z, 2y - z) -> a) Find the standard matrix A for the linear transformation T. b) Use A to find the image of the vector v = (0,1,1).
2. Given the matrix A = [6] and P = [1
find A5 using a diagonal matrix D = P-1 AP.
Transcribed Image Text:2. Given the matrix A = [6] and P = [1 find A5 using a diagonal matrix D = P-1 AP.
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